Here's a clean explanation from NASA's eclipse site (https://eclipse2017.nasa.gov/why-do-eclipse-tracks-move-east...).

The moon actually moves much faster than the Earth spins -- it just seems to move westward to humans on the ground because it's so far away from Earth (takes 28 days to go around Earth). During a solar eclipse though, we see the effect of its true blisteringly fast orbital speed.

"Because the Moon moves to the east in its orbit at about 3,400 km/hour. Earth rotates to the east at 1,670 km/hr at the equator, so the lunar shadow moves to the east at 3,400 – 1,670 = 1,730 km/hr near the equator. You cannot keep up with the shadow of the eclipse unless you traveled at Mach 1.5."